Question: Simplify the following expression: $ z = \dfrac{t + 6}{t - 9} - \dfrac{-6}{5} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{t + 6}{t - 9} \times \dfrac{5}{5} = \dfrac{5t + 30}{5t - 45} $ Multiply the second expression by $\dfrac{t - 9}{t - 9}$ $ \dfrac{-6}{5} \times \dfrac{t - 9}{t - 9} = \dfrac{-6t + 54}{5t - 45} $ Therefore $ z = \dfrac{5t + 30}{5t - 45} - \dfrac{-6t + 54}{5t - 45} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{5t + 30 - (-6t + 54) }{5t - 45} $ Distribute the negative sign: $z = \dfrac{5t + 30 + 6t - 54}{5t - 45}$ $z = \dfrac{11t - 24}{5t - 45}$